Question

Assume that the probability of a defective computer component is 0.02. Components are randomly selected. Find the probability that the first defect is caused by the seventh component tested. How many components do you expect to test until one is found to be defective?

Answer 1

Let X denote the number of computer components tested until we get the first defective.

The probability of getting a defective computer component is 0.02. Say p= 0.02

According to the definition of a Geometric random variable we can say that X follows Geometric distribution with the parameter p= 0.02.

P[X= x] = p* (1-p)^x-1

We need to find the probability that the first defect is caused by the seventh component tested.

= P[X= 7] = p* (1-p)^7-1 = 0.02*(1-0.02)⁶ = 0.0177

Hence, the probability that the first defect is caused by the seventh component tested is 0.0177.

Expected number of components to test until one is found to be defective

= E( X ) = 1/p = 1/0.02 = 50

Hence, We expect 50 components to test until one is found to be defective.

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